TAOISEACH Leo Varadkar and Theresa May are expected to make a decision on whether to persevere with the Stormont talks before the end of the week.
The latest round of negotiations aimed at restoring the devolved institutions began earlier this month.
Expectations of an early breakthrough are low, though the process is expected to intensify this week now that the European election is completed.
Tanáiste Simon Coveney and Secretary of State Karen Bradley will meet the party leaders today in Belfast before taking stock of any progress to date.
They are expected to brief their respective leaders, making recommendations on where the process is likely to go.
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A number of working groups chaired by serving and retired senior civil servants looking at various issues relating to any restored institutions will continue to hold a series of meetings throughout this week.
An Dublin government spokesman told The Irish News that Mrs May's decision to step down as Tory leader was not expected to impact on how the two leaders chose to take forward the negotiations.
The spokesman repeated the desire of the Republic's government to see devolution restored.
"The Irish government does not want to see a return to direct rule, we want the institutions restored as soon as possible," the spokesman said.
There has been no devolved government in the north since January 2017, when the late Martin McGuinness collapsed the institutions when he resigned as deputy first minister at the height of public outcry over the Renewable Heat Incentive scandal.
The DUP walked away from a draft deal at the eleventh hour in February last year after disquiet in its ranks over provisions for an Irish language act.
